Answers by Carol B.

You want to build a cement walk around a 24 ft x 49 ft garden
If we let x = the width of the cement walk, then the outside dimensions of the walk will be
(24 + 2x) and (49 + 2x)
The garden itself will not be covered with cement, so the equation for the area of the walk...

You can use the midpoint formula, knowing the midpoint between two points (x1,y1) and (x2,y2) has the coordinates
[(x1 + x2)/2, (y1 + y2)/2]
Substituting what we are given, we get:
(2 + x2)/2 = 5 and (5 + y2)/2 = 1
so,
2...

First, see that 80 liters of a 20% kool aid solution has 16 liters of kool aid, since 80x20% = 16
Now, we're going to add an amount of 59% kool aid to produce a total concentration of 30% kool aid.
So you can set it up as a proportion. Let x = number of liters...

To solve this equation, manipulate the numbers so that the base numbers are the same. Since 4 = 2^2 we can rewrite this as:
2^3x = (2^2)^(x+2)
Expanding the exponent gives:
2^3x = 2^(2x+4)
Now that both bases are the same, we see that
3x = 2x+4
Solving...

To solve this equation for x, we should simplify and then combine like terms.
Notice that the second term, 8x/x, simplifies to 8 since x/x = 1, so we can rewrite the equation as:
4-8+1 = 8/x+1
Combining the constant terms gives:
-3 = 8/x +1
To get the x...

Notice that you can factor a 2 from the numerator to get
[2(x^2 + 2x +1)]/(x^2 + 3x +2)
Next, we factor both numerator and denominator to get
[2(x+1)(x+1)]/(x+1)(x+2)
Cancelling (x+1) from both numerator and denominator gives
[2(x+1)]/...

Since you are give three zeros, we know we have a 3rd degree polynomial. Recall that we factor a polynomial in the form of:
(x-a)(x-b)(x-3) = 0
where a, b, and c are the zeros of the function.
Thus, your function factors as:
(x+5)(x+1)(x-2) = 0
Doing this...